The divisors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The divisors of 24 are those numbers that divide 24 entirely without a remainder. In this section, we will discuss divisors of 24.
Table of Contents
Highlights of Divisors of 24
- Divisors of 24: 1, 2, 3, 4, 6, 8, 12 and 24
- Negative divisors of 24: -1, -2, -3, -4, -6, -8, -12 and -24
- Prime divisors of 24: 2 and 3
- Number of divisors of 24: 8
- Sum of divisors of 24: 60
- Product of divisors of 24: 244
What are Divisors of 24
A number n is called a divisor of 24 if the fraction $\dfrac{24}{n}$ is an integer. Note that if 24/n=m is an integer, then both m and n will be the divisors of 24.
To find the divisors of 24, we need to find the numbers n such that 24/n becomes an integer. We have:
| 24/1=24 | 1, 24 are divisors of 24. |
| 24/2=12 | 2, 12 are divisors of 24 |
| 24/3=8 | 3, 8 are divisors of 24 |
| 24/4=6 | 4, 6 are divisors of 24 |
No numbers other than 1, 2, 3, 4, 6, 8, 12, and 24 can divide 24. So we conclude that
|
The divisors of 24 are: 1, 2, 3, 4, 6, 8, 12, and 24. |
Thus, the total number of divisors of 24 is eight.
Negative Divisors of 24
We know that if m is a divisor of a number, then -m is also a divisor of that number.
As the divisors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24, we can say that:
The negative divisors of 24 are -1, -2, -3, -4, -6, -8, -12, and –24.
Prime Divisors of 24
The divisors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. Among these numbers, only 2 and 3 are prime numbers. So we obtain that:
The prime divisors of 24 are 2 and 3.
Video solution of Divisors of 24:
Sum, Product & Number of Divisors of 24
The prime factorization of 24 is given below.
24 = 23 × 31
(i) By the number of divisors formula, we have that the number of divisors of 24 is
=(3+1)(1+1)=4×2=8.
(ii) By the sum of divisors formula, we have that the sum of the divisors of 24 is
$=\dfrac{2^4-1}{2-1} \times \dfrac{3^2-1}{3-1}$
$=\dfrac{16-1}{1} \times \dfrac{9-1}{2}$
$=15 \times 4=60$
(iii) By the product of divisors formula, we have that the product of the divisors of 24 is
=24(Number of divisors of 24)/2
=248/2
=244
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FAQs
Answer: The divisors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
Answer: The product of all divisors of 24 is =24(Number of divisors of 24)/2 =248/2 = 244.
Answer: The sum of all divisors of 24 is equal to 60.
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